Compound of five truncated cubes explained

bgcolor=#e7dcc3 colspan=2	Compound of five truncated cubes
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Type	Uniform compound
Index	UC57
Polyhedra	5 truncated cubes
Faces	40 triangles, 30 octagons
Edges	180
Vertices	120
Symmetry group	icosahedral (Ih)
Subgroup restricting to one constituent	pyritohedral (Th)

This uniform polyhedron compound is a composition of 5 truncated cubes, formed by truncating each of the cubes in the compound of 5 cubes.

Cartesian coordinates

Cartesian coordinates for the vertices of this compound are all the cyclic permutations of

(±(2+), ±, ±(2+))

(±τ, ±(τ⁻¹+τ⁻¹), ±(2τ−1+τ))

(±1, ±(τ⁻²−τ⁻¹), ±(τ²+τ))

(±(1+), ±(−τ⁻²−), ±(τ²+))

(±(τ+τ), ±(−τ⁻¹), ±(2τ−1+τ⁻¹))

where τ = (1+)/2 is the golden ratio (sometimes written φ).

References

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